The ability to send out a companion on missions is not tied to your level. However, doing this route as you suggest, will only allow you to have 1 companion doing these missions. By the time you hit the level cap, you will have 6 companions (including the ship droid), 5 of which can be out doing missions or crafting items at the same time.

The number of companions you have obviously increases as you progress through the story, and the number you can have out at a time IS tied to your character level, so it's more likely that anyone with a "crafting alt" will end up leveling it up anyway, because it's just more efficient to have more companions out doing your bidding.